March 11, 1904.] 



SCIENCE. 



40-6 



as a voluntary exile to Italy, settled at 

 Croton (as Ovid mentions), and there cre- 

 ated and taught new and sublimer hypoth- 

 eses for our universe. The most diversely 

 demonstrated and frequently applied theo- 

 rem of geometry bears his name. The first 

 solution of a problem in that most subtle 

 and final of ways, by proving it impossible, 

 is due to him; his solution of the problem 

 to find a common submxiltiple of the hy- 

 pothenuse and side of an isosceles right 

 triangle, an achievement whereby he cre- 

 ated incommensurability. 



It is noteworthy that this making of in- 

 commensurables is confused by even the 

 most respectable of the historians of mathe- 

 matics with the creation of irrational num- 

 bers. But in the antique world there were 

 no such numbers as the square root of two 

 or the square root of three. Such num- 

 bers can not be discovered, and it was cen- 

 turies before they were created. The 

 Greeks had only rational numbers. 



3. EUCLID. 



Under the Horseshoe Falls at Niagara 

 press on beyond the guide; risk life for 

 the magnificent sensation of a waterspout, 

 a cloudburst, an avalanche, a tumbling 

 cathedral of waterblocks! It must end in 

 an instant, this extravagant downpour of 

 whole wealths of water. Then out; and 

 look away down the glorious canyon, and 

 read in that graven history how this mo- 

 mentary riotous chaos has been just so, 

 precisely the same, for centuries, for ages, 

 for thousands of years. 



In the history of science a like antithesis 

 of sensations is given by Euclid's geometry. 



In the flood of new discovery and rich 

 advance recorded in books whose mere 

 names woxild fill volumes, we ask ourselves 

 how any one thing can be permanent? 

 Yet, looking back, we see this Euclid not 

 only cutting his resistless way through the 

 rock of the two thousand years that make 



the history of the intellectual world, but, 

 what is still more astounding, we find that 

 the profoundest advance of the last two 

 centuries has only served to emphasize the 

 consciousness of Euclid's perfection. 



Says Lyman Abbott, if you want an in- 

 fallible book go not to the Bible, but to 

 Euclid. 



In 'The Wonderful Century,' Alfred 

 Russel Wallace says, speaking of all time 

 before the seventeenth century : ' ' Then go- 

 ing backward, we can find nothing of the 

 first rank except Euclid's wonderful sys- 

 tem of geometry, perhaps the most remark- 

 able product of the earliest civilizations." 



Says Professor Alfred Baker, of the Uni- 

 versity of Toronto: "Of the perfection of 

 Euclid (B. C. 290) as a scientific treatise, 

 of the marvel that such a work could have 

 been produced two thousand years ago, I 

 shall not here delay to speak. I content 

 myself with making the claim that, as a 

 historical study, Euclid is, perhaps, the 

 most valuable of those that are taken up 

 in our educational institutions." 



At its very birth this typical product of 

 the Greek genius assumed sway over the 

 pure sciences. In its first efflorescence, 

 through the splendid days of Theon and 

 Hypatia, fanatics could not murder it as 

 they did Hypatia, nor later could that dis- 

 mal flood, the dark ages, drown it. Like 

 the phcenix of its native Egypt it rises 

 anew with the new birth of culture. An 

 Anglo-Saxon, Adelhard of Bath, finds it 

 clothed in Arabic vestments in the Moorish 

 land of the Alhambra. 



In 1120, Adelhard, disguised as a Mo- 

 hammedan student, went to Cordova, ob- 

 tained a Moorish copy of Euclid's 'Ele- 

 ments,' and made a translation from the 

 Arabic into Latin. 



The first translation into English (1570) 

 was made by 'Henrieus Billingsley, ' after- 

 M'ard Sir Henry Billingsley, Lord Mayor 

 of London, 1591. And up . to this very 



